206 THE REFRACTION OF SOUND. 



resistances, the course of the boat would be changed, or •'refracted." 

 This image may be taken as a rough ilhistration of the phenomenon of 

 "refraction" generally. 



There are three different methods in which sound-waves passing 

 through a gaseous medium may suffer such unequal disturbance of 

 velocity: first, by variations of density in the medium, sound moving 

 more slowly through a dense air than a rare one, the pressure being the 

 same 5 second, by variations of elasticity in the medium, sound moving 

 more swiftly with increase of elasticity, the density being the same ; 

 and, third, by variations of motion or current in the medium, sound trav- 

 eling by convection faster with the wind by a small percentage, accord- 

 ing to its velocity, and more slowly against the wind.* 



There is no doubt that light also would be subject to all three of these 

 forms of refraction, as its velocity is necessarily retarded by an increase 

 of density in the medium, by a reduction of the elasticity of the medium, 

 and by an adverse motion of the medium. 



A fourth cause of velocity disturbance in the case of sound is found 

 in the temperature of the medium, sound moving more swiftly in a heated 

 atmosphere than in a cooler one. This cause of acoustic refraction is 

 practically a highly important one; though it may be theoretically 

 resolved into one of the preceding conditions, since the only dynamic 

 effect of heat on a gas is to increase its elasticity if the volume be con- 

 stant by confinement, or to increase its volume if unconfined without 

 changing its elasticity. 



The relation of these atmospheric conditions to each other is exceed- 

 ingly simple. 



The density of a perfect gas (the inverse of its volume) varies directly 

 as the pressure, the temperature being constant, or inversely as the 

 absolute temperature, the pressure being constant. 



The elasticity of a perfect gas varies directly as the pressure, the den- 

 sity being constant, or inversely as the density, the pressure being con- 

 stant. It also varies directly as the absolute temperature, the volume 

 being constant.t 



From these relations it follows that increase of atmospheric pressure 

 does not affect the velocity of sound; ibr although the density is directly 

 proportional to the pressure, and this diminishes the velocity, yet as the 

 elasticity is also directly proportional to the pressure, and this increases 

 the velocity by precisely the same amount, the two effects are neutral- 

 ized. 



*The ratio of the velocity of the wind to that of sound (one or two per cent.) is too 

 small to 1)0 of any account directh/. Differentially, it becomes very important. A uni- 

 form wind has no practical effect on sound except to slightly llatten or lower the pitch 

 in its own direction, and to sharj)eu or raise the pitch in tl)e opposite direction. 



t According to Waterston, "when air is compressed or dilated, the absolute tempera- 

 ture varies as the cube root of the density, and the tension as the fourth power of tlio 

 absolute temperature, or cube root of the fourth power of the density," {Iiep. Brit. 

 Assoc, lb53, J). 1'^ of Abstracts.) This would indicate a striking departure from the 

 condition of a perfect gas. 



